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I cleaned the hole out and then used something like this (not this exact one though) for the same issue before. https://www.amazon.co.uk/fischer-539461-Injection-Resin-Clear/dp/B07W9LZFZ5?psc=1
You might also get away with using wetnfix with deeper plugs so that you get to some solid wall behind (EDIT - seems unlikely given your later post).
But if it's for a survey and being sold why not get something cheap and light?
I think it’s beyond a wooden plug